This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ME 375 Homework 2 : Solution October 6, 2009 Problem 1 Derive the equation of motion for the system shown, state any assumptions and draw the free body diagrams. Figure 1: Problem 1 1 Solution: The free body diagram is as follows: Figure 2: Problem 1FBD Assumptions: • The spring is massless and acts as an ideal spring • The cord only moves vertical • The two disks are both fixed together and only rotate around one point O • Assume no slipping Explanation of symbols used: • x : displacement of static equilibrium for the mass m • y : displacement of static equilibrium for the spring • θ : the angular displacement of the disk • F s : force • F k : spring force Solution: First, we know that the disk has an angular position θ . We can correlate this 2 to x and y as follows: x = Rθ y = 4 Rθ We have the following equations: For the mass m: m ¨ x = F s (1) For the disk J: J ¨ θ = RF s + 4 RF k (2) F k = ky (3) We also know the correlation between θ and x...
View
Full Document
 Fall '10
 Meckle
 Force, Friction

Click to edit the document details